diff --git a/dune/mmdg/mmdg.hh b/dune/mmdg/mmdg.hh
index e881d5e45fce9c20c5f45b69dccb2b95fabc3e67..4d58fd3c12ffb5349624ddf9df763cdf209b4104 100644
--- a/dune/mmdg/mmdg.hh
+++ b/dune/mmdg/mmdg.hh
@@ -133,7 +133,7 @@ private:
     //in total we use the basis given by the union of
     // { (phi_elem,i , 0) | elem in elements(gridView), i = 0,...,dim }
     //and
-    // { (0 , phi_iElem,i ) | iElem in elements(iGridView), i = 0,...,dim-1 }
+    // { (0 , phi_iElem,i) | iElem in elements(iGridView), i = 0,...,dim-1 }
 
     //thus the stiffness matrix A and the load vector b exhibit the following
     //block structure
diff --git a/dune/mmdg/problems/mmdgproblem4.hh b/dune/mmdg/problems/mmdgproblem4.hh
index 50777e829fe6f3ccc05b2fae67eefde119346c4e..61d19dc60b91ff31607991fcdbfd3110b199175c 100644
--- a/dune/mmdg/problems/mmdgproblem4.hh
+++ b/dune/mmdg/problems/mmdgproblem4.hh
@@ -32,7 +32,6 @@ public:
   //the exact solution on the interface at position pos
   Scalar exactInterfaceSolution (const Coordinate& pos) const
   {
-    //return 1.5;
     return pos[0] * pos[0] - pos[1] * pos[1] + 0.5 * d_;
   }
 
@@ -51,7 +50,7 @@ public:
   //interface source term at position pos
   Scalar qInterface (const Coordinate& pos) const
   {
-    return 2.0 * d_; //d^2
+    return 2.0 * d_;
   }
 
   //aperture d of the fracture at position pos
@@ -76,7 +75,6 @@ public:
       permeability[i][i] = 1.0 / d_;
     }
 
-    //return identity matrix
     return permeability;
   }
 
diff --git a/dune/mmdg/problems/mmdgproblem5.hh b/dune/mmdg/problems/mmdgproblem5.hh
new file mode 100644
index 0000000000000000000000000000000000000000..0a3ad3d11a558330a941ee54917bc3f671e50b37
--- /dev/null
+++ b/dune/mmdg/problems/mmdgproblem5.hh
@@ -0,0 +1,128 @@
+#ifndef __DUNE_MMDG_MMDGPROBLEM5_HH__
+#define __DUNE_MMDG_MMDGPROBLEM5_HH__
+
+#include <cmath>
+#include <dune/mmdg/problems/coupleddgproblem.hh>
+
+//a coupled dg problem
+template<class Coordinate, class Scalar = double>
+class MMDGProblem5 : public CoupledDGProblem<Coordinate, Scalar>
+{
+public:
+  static constexpr int dim = Coordinate::dimension;
+  using Base = CoupledDGProblem<Coordinate, Scalar>;
+  using Matrix = typename Base::Matrix;
+
+  //constructor
+  MMDGProblem5 (const Scalar d) : d_(d) {}
+
+  //the exact bulk solution at position pos
+  Scalar exactSolution (const Coordinate& pos) const
+  {
+    return (pos[1] > pos[0]) ?
+      1.0 / (1.0 + pos[0] * pos[0]) : -1.0 / (1.0 + pos[1] * pos[1]);
+  }
+
+  //the exact solution on the interface at position pos
+  Scalar exactInterfaceSolution (const Coordinate& pos) const
+  {
+    return 0.0;
+  }
+
+  //indicates whether an exact solution is implemented for the problem
+  bool hasExactSolution () const
+  {
+    return true;
+  };
+
+  //source term at position pos
+  Scalar q (const Coordinate& pos) const
+  {
+    const Scalar x2Plus1 = pos[0] * pos[0] + 1.0;
+    const Scalar y2Plus1 = pos[1] * pos[1] + 1.0;
+
+    return (pos[1] > pos[0]) ?
+      -4.0 * pos[0] / (x2Plus1 * x2Plus1) : 4.0 * pos[1] / (y2Plus1 * y2Plus1);
+  }
+
+  //interface source term at position pos
+  Scalar qInterface (const Coordinate& pos) const
+  {
+    return 0.0;
+  }
+
+  //aperture d of the fracture at position pos
+  Scalar aperture (const Coordinate& pos) const
+  {
+    return d_;
+  }
+
+  //permeability tensor at position pos
+  Matrix K (const Coordinate& pos) const
+  {
+    Matrix permeability(0.0);
+
+    for (int i = 0; i < dim; i++)
+    {
+      permeability[i][i] = pos[i] + 1.0 / pos[i];
+    }
+
+    return permeability;
+  }
+
+  //permeability of the fracture in normal direction at position pos
+  Scalar Kperp (const Coordinate& pos) const
+  {
+    constexpr Scalar Kvalue = 1.0 / sqrt(2.0);
+    return Kvalue;
+  }
+
+  //tangential permeability tensor of the interface at position pos
+  Matrix Kparallel (const Coordinate& pos) const
+  {
+    Matrix permeability(0.0);
+    Scalar y2Plus1_2 = 1.0 + pos[1] * pos[1];
+    y2Plus1_2 *= y2Plus1_2;
+
+    for (int i = 0; i < dim; i++)
+    {
+      permeability[i][i] = y2Plus1_2;
+    }
+
+    return permeability;
+  }
+
+  //returns the recommended quadrature order to compute an integral
+  //over x * boundary(x)
+  int quadratureOrderBoundary () const
+  {
+    return 10;
+  }
+
+  //returns the recommended quadrature order to compute an integral
+  //over x * interfaceBoundary(x)
+  int quadratureOrderInterfaceBoundary () const
+  { //NOTE: only relevant for 3d, not implemented!
+    return 10;
+  }
+
+  //returns the recommended quadrature order to compute an integral
+  //over x * qInterface(x)
+  int quadratureOrder_qInterface () const
+  {
+    return 10;
+  }
+
+  //returns the recommended quadrature order to compute an integral
+  //over x * q(x)
+  int quadratureOrder_q () const
+  {
+    return 10;
+  }
+
+private:
+  Scalar d_; //aperture
+
+};
+
+#endif
diff --git a/src/grids/mmdg5.geo b/src/grids/mmdg5.geo
new file mode 100644
index 0000000000000000000000000000000000000000..d13f9ab8cd101a5dd0289069232482975d1587ae
--- /dev/null
+++ b/src/grids/mmdg5.geo
@@ -0,0 +1,27 @@
+//characteristic length
+lc = 8e-2;
+
+//domain corners, domain = [0,1] x [0,1]
+Point(1) = {1, 1, 0, lc};
+Point(2) = {2, 1, 0, lc};
+Point(3) = {2, 2, 0, lc};
+Point(4) = {1, 2, 0, lc};
+
+//domain outline
+Line(1) = {1, 2};
+Line(2) = {2, 3};
+Line(3) = {3, 4};
+Line(4) = {4, 1};
+
+//interface outline
+Line(5) = {1,3};
+
+//curve loops
+Curve Loop(1) = {1:4}; //domain boundary
+
+//surfaces
+Plane Surface(1) = {1};
+Physical Surface(1) = {1};
+
+Curve{5} In Surface{1};
+Physical Curve(2) = {5};
diff --git a/src/grids/mmdg5_1.msh b/src/grids/mmdg5_1.msh
new file mode 100644
index 0000000000000000000000000000000000000000..f66babb60a94f99b0e3742f6338a8c4c320cc628
--- /dev/null
+++ b/src/grids/mmdg5_1.msh
@@ -0,0 +1,20 @@
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diff --git a/src/grids/mmdg5_2e-1.msh b/src/grids/mmdg5_2e-1.msh
new file mode 100644
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diff --git a/src/grids/mmdg5_5e-1.msh b/src/grids/mmdg5_5e-1.msh
new file mode 100644
index 0000000000000000000000000000000000000000..f5c5415e77a1946b7529c3e665534bc12d7ba246
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diff --git a/src/grids/mmdg5_5e-2.msh b/src/grids/mmdg5_5e-2.msh
new file mode 100644
index 0000000000000000000000000000000000000000..ef0f0c2641b6f8bd2c121e9a6b1a0f8eb48268c6
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diff --git a/src/grids/mmdg5_8e-2.msh b/src/grids/mmdg5_8e-2.msh
new file mode 100644
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diff --git a/src/mmdg.cc b/src/mmdg.cc
index 20d7d6de0762ab0e1d9ae12edd65b5b65976439d..894c3044684293d6a78f6c7bdf46c0387cd4122e 100644
--- a/src/mmdg.cc
+++ b/src/mmdg.cc
@@ -24,6 +24,7 @@
 #include <dune/mmdg/problems/mmdgproblem2.hh>
 #include <dune/mmdg/problems/mmdgproblem3.hh>
 #include <dune/mmdg/problems/mmdgproblem4.hh>
+#include <dune/mmdg/problems/mmdgproblem5.hh>
 
 int main(int argc, char** argv)
 {
@@ -82,6 +83,11 @@ int main(int argc, char** argv)
       problem = new MMDGProblem4<Coordinate>(aperture);
       gridType = "mmdg2_5e-2";
     }
+    else if (pt["problem"] == "mmdg5")
+    {
+      problem = new MMDGProblem5<Coordinate>(aperture);
+      gridType = "mmdg5_5e-2";
+    }
     else
     {
       DUNE_THROW(Dune::Exception,
diff --git a/src/mmdgAnalysis.py b/src/mmdgAnalysis.py
index c66dd514341f1a88a1b75593be2f175655f24a4b..89c1f6e9214ab090e843489e82ed89c44bdd929f 100644
--- a/src/mmdgAnalysis.py
+++ b/src/mmdgAnalysis.py
@@ -63,6 +63,7 @@ numberOfMeans = 1
 # names of the grid files sorted by refinement
 gridfiles = ["mmdg2_1", "mmdg2_5e-1", "mmdg2_2e-1", "mmdg2_8e-2", "mmdg2_5e-2"]
 # gridfiles = ["mmdg3_1", "mmdg3_5e-1", "mmdg3_2e-1", "mmdg3_8e-2", "mmdg3_5e-2"]
+# gridfiles = ["mmdg5_1", "mmdg5_5e-1", "mmdg5_2e-1", "mmdg5_8e-2", "mmdg5_5e-2"]
 
 dim = 2
 
diff --git a/src/parameterMMDG.ini b/src/parameterMMDG.ini
index a6283fc3114613f0a0e3f66adc1fcb6338c5992e..d214f65a5b92af753727c8050b00ed0444bc76c1 100644
--- a/src/parameterMMDG.ini
+++ b/src/parameterMMDG.ini
@@ -1,5 +1,5 @@
 mu = 1000
 xi = 0.75
+d = 1
 problem = mmdg2
 gridfile = mmdg2_5e-2
-d = 1